Parallel Solver Research Articles

MPI/OpenMP-Based Parallel Solver for Imprint Forming Simulation

MPI/OpenMP-Based Parallel Solver for Imprint Forming Simulation

DEVELOPING SITUATIONAL CONDITIONS AND PROGRAM CODES FOR PARALLEL SITUATIONAL ANALYSIS SOLVER BASED ON CONIC UMBRA/SUNLIT MODELS

The search for optimal time intervals for satellite operations performance is based on verifying specific conditions of geometric or physical nature. Several conditions are combined in a situational problem. To be able to solve different situational problems, it is necessary to develop program codes for verifying different situational conditions in advance. Two situational conditions for determining if the satellite is in the sunlit zone or the umbra based on the conical models of the earth's shadow are presented. Necessary (but not sufficient) conditions are introduced to locate the satellite in the umbra or the sunlit zone, respectively. These conditions simplify the calculations and increase the computational efficiency for a large part of the satellite orbit. Problems with one or more conditions are solved by a developed parallel solver for situational analysis. Conditions checking the position of a satellite relative to the Earth's shadow can be combined with other situational conditions. A model of description of situational conditions is shown.

Fast Parallel Solver of Time-harmonic Wave Equation with Topography

Fast Parallel Solver of Time-harmonic Wave Equation with Topography

Investigation of the lattice Boltzmann method to resolve combined radiation-conduction heat transfer in participating media with curved boundaries

PurposePresent study aims to extend the lattice Boltzmann method (LBM) to simulate radiation in geometries with curved boundaries, as the first step to simulate radiation in complex porous media. In recent years, researchers have increasingly explored the use of porous media to improve the heat transfer processes. The lattice Boltzmann method (LBM) is one of the most effective techniques for simulating heat transfer in such media. However, the application of the LBM to study radiation in complex geometries that contain curved boundaries, as found in many porous media, has been limited.Design/methodology/approachThe numerical evaluation of the effect of the radiation-conduction parameter and extinction coefficient on temperature and incident radiation distributions demonstrates that the proposed LBM algorithm provides highly accurate results across all cases, compared to those found in the literature or those obtained using the finite volume method (FVM) with the discrete ordinates method (DOM) for radiative information.FindingsFor the case with a conduction-radiation parameter equal to 0.01, the maximum relative error is 1.9% in predicting temperature along vertical central line. The accuracy improves with an increase in the conduction-radiation parameter. Furthermore, the comparison between computational performances of two approaches reveals that the LBM-LBM approach performs significantly faster than the FVM-DOM solver.Originality/valueThe difficulty of radiative modeling in combined problems involving irregular boundaries has led to alternative approaches that generally increase the computational expense to obtain necessary radiative details. To address the limitations of existing methods, this study presents a new approach involving a coupled lattice Boltzmann and first-order blocked-off technique to efficiently model conductive-radiative heat transfer in complex geometries with participating media. This algorithm has been developed using the parallel lattice Boltzmann solver.

Parallel scalability of sparse solvers for sparsified fractional diffusion problems discretized with FEM

Anomalous diffusion is a non-local process that describes a wide spectrum of natural processes and phenomena with many applications in science and technology. It is described mathematically by the fractional Laplace operator. In this work we examine the integral definition of the fractional Laplacian modeled with the Riesz potential and discretized with the finite element method. The thus obtained system of linear algebraic equations is dense due to the non-local nature of the fractional Laplacian and is computationally complex to solve. With LU factorization, for example, solving the problem has an O(N 3) computational complexity, where N is the number of unknowns. However, it can be observed that a large amount of the off-diagonal coefficients have very small absolute values compared to the diagonal coefficients. Those small off-diagonal coefficients can be lumped (set to zero and added to the diagonal coefficient) without significant loss of accuracy. In this work we employ a direct sparse parallel solver to the resultant sparse matrix. We analyze the parallel performance and speed-up, as well as the accuracy, varying the fractional power and the lumping threshold.

Massively parallel nodal discontinous Galerkin finite element method simulator for room acoustics

We present a massively parallel and scalable nodal discontinuous Galerkin finite element method (DGFEM) solver for the time-domain linearized acoustic wave equations. The solver is implemented using the libParanumal finite element framework with extensions to handle curvilinear geometries and frequency dependent boundary conditions of relevance in practical room acoustics. The implementation is benchmarked on heterogeneous multi-device many-core computing architectures, and high performance and scalability are demonstrated for a problem that is considered expensive to solve in practical applications. In a benchmark study, scaling tests show that multi-GPU support gives the ability to simulate large rooms, over a broad frequency range, with realistic boundary conditions, both in terms of computing time and memory requirements. Furthermore, numerical simulations on two non-trivial geometries are presented, a star-shaped room with a dome and an auditorium. Overall, this shows the viability of using a multi-device accelerated DGFEM solver to enable realistic large-scale wave-based room acoustics simulations.

High-Fidelity Simulations of Shield Assembly Mixed-Convection Flows with Applications Toward Reduced-Resolution Modeling

Flow circulation and heat removal through shield and reflector assemblies can have major impacts on safety in long transients for sodium fast reactors (SFRs). These transients are typically categorized by reduced flow rates and large-scale organized flow patterns, including potential intra-assembly circulation. Such low-flow cases can provide challenges for experiments because of complications in measuring the flow rates and temperatures with high accuracy in different areas. This consequently also raises the uncertainty of many modeling approaches for these phenomena. In an effort to address some of these issues, high-fidelity large eddy simulations are performed using the highly parallel solver NekRS. A 19-pin configuration of a tight-lattice wire-wrapped hexagonal bundle (pitch-to-diameter ratio = 1.07), representing a prototypical internal configuration of a shield assembly, was investigated. The sodium flow was set at a bundle Reynolds number of 2000, with simulations being performed for modified Richardson numbers of 0.0 (i.e., no buoyancy), 0.01, and 0.04, where mixed-convection effects are anticipated. The flow and temperature fields for these cases are discussed in detail. The high-fidelity data should prove useful as reference data for expanding and improving on various reduced-resolution approaches. A basic framework for combining subchannel and computational fluid dynamics methodologies in SFRs is also presented, with preliminary results from simulations of light water reactor bundles and a discussion of changes that need to be made for potential application to SFRs.

Numeričko istraživanje utjecaja zakrilaca krmenog praga na hidrodinamičke performanse glisiranja

The trim tab and interceptor have been utilized to optimize the running trim and motion control of planing boats at varying speeds in calm water. Increasing the height of the interceptor can create excessive drag and bow-down trim. The effectiveness of the interceptor can be increased by integrating it with a horizontal flap. This research focuses on the impact of the influence caused by interceptor flaps on the pressure distribution and fluid flows around the vessel. To simulate trim and sinkage measurement, the environment was modeled in the two-degree of freedom condition. Variation of integrated interceptor flaps has been analyzed with Finite Volume Method (FVM) based on RANS (Reynolds-Averaged Navier-Stokes) equation using overset mesh. The turbulent K- ε and VOF (Volume of Fluid) models are used to model the water and air phases. The grid convergence study is performed to establish the parallel solver’s grid independence. To confirm the accuracy of the test in the bare hull condition, the numerical approach was tested experimentally. The result of drag, trim, and sinkage was calculated and it has been proved that the added flaps into interceptors are very useful in drag reduction and trim control. The percentage of interceptor height is directly proportional to the resulting lift force. Higher lift force can more effectively improve trim and reduce drag. Overall, this study shows an improvement in ship performance when using an interceptor and interceptor flap. One of the model configurations in the study has been shown to reduce drag by up to 33.3% at Froude number 1.45 when compared to ships without an interceptor.

High performance calculation of nonlinear wave propagation on GPU for focused ultrasound treatment planning

High intensity focused ultrasound (HIFU) is very promising new technology that has many therapeutic application, and among them are the treatment of cancer in different organs without major side effects. Some of the limitations of HIFU are the long treatment time and incomplete ablation. High performance computing can help in this regard. Simulation of nonlinear wave propagation in three dimensional geometry is very time consuming process especially when shocks are presented. In the current work, we are going to present three dimensional parallel solver on GPU. Some examples for the simulation in a patient specific geometry will be also presented. The presented results can be used for the optimization of the treatment. For the validation of the results, ex-vivo and in-vivo experiments have been performed. It has been shown that large volume can be ablated within a short period of time.

A parallel strategy applied to the simplified thermal-hydraulic part of system program

To meet the requirements of real-time data processing and massive computation, it is necessary to introduce the parallel strategy into the System Thermal-Hydraulic part of System Program (STHSP) to increase computing speed. In this paper, an in-house parallel solver named STHSP-MPI was developed based on Message Passing Interface (MPI) method. Two-phase flow problems were solved by using the finite volume method and the Newton-Raphson algorithm. Firstly, validations of present parallel solver were performed quantitatively through several benchmark tests. Then, the computational efficiency was quantitatively described by speedup ratio and time overheads. Furthermore, the performances of parallel solver and program with adaptive mesh refinement were compared in detail. The simulation results show that the parallel strategy can significantly improve the computational performance of the system program while ensuring the accuracy.

Uncertainty quantification in coastal aquifers using the multilevel Monte Carlo method

AbstractWe are solving a problem of salinisation of coastal aquifers. As a test case example, we consider the Henry saltwater intrusion problem. Since porosity, permeability and recharge are unknown or only known at a few points, we model them using random fields and random variables. The Henry problem describes a two‐phase flow and is non‐linear and time‐dependent. The solution to be found is the expectation of the salt mass fraction, which is uncertain and time‐dependent. To estimate this expectation, we use the well‐known multilevel Monte Carlo (MLMC) method. The MLMC method takes just a few samples on computationally expensive (fine) meshes and more samples on cheap (coarse) meshes. Then, by building a telescoping sum, the MLMC method estimates the expected value at a much lower computational cost than the classical Monte Carlo method. The deterministic solver used here is the well‐known parallel and scalable ug4 solver.

Adaptive economic predictive control for offshore wind farm active yaw considering generation uncertainty

Inevitable model uncertainty could render active yaw control (AYC) to make suboptimal or even irrational decisions. To this end, this paper quantitatively analyzes the influential mechanisms of uncertainty on optimal yaw policy in terms of the wake model and power model. In order to address power model uncertainty that has received little attention in the AYC field, this paper proposes an efficient adaptive economic predictive control. This framework begins with the construction of a neural network-based compensator to provide online adaptive estimation of parameter uncertainty. On this basis, an adaptive economic predictive control with the economic objective of maximizing the total power is designed to increase the confidence of yaw policy in the presence of generation uncertainty, and a parallel heuristic solver is developed to allow real-time control of large-scale wind farms. Finally, extensive results based on three wind farm cases demonstrate the effectiveness and advantages of the proposed control strategy.

Development of a parallel multiscale 3D model for thrombus growth under flow

Thrombus growth is a complex and multiscale process involving interactions spanning length scales from individual micron-sized platelets to macroscopic clots at the millimeter scale. Here, we describe a 3D multiscale framework to simulate thrombus growth under flow comprising four individually parallelized and coupled modules: a data-driven Neural Network (NN) that accounts for platelet calcium signaling, a Lattice Kinetic Monte Carlo (LKMC) simulation for tracking platelet positions, a Finite Volume Method (FVM) simulator for solving convection-diffusion-reaction equations describing agonist release and transport, and a Lattice Boltzmann (LB) flow solver for computing the blood flow field over the growing thrombus. Parallelization was achieved by developing in-house parallel routines for NN and LKMC, while the open-source libraries OpenFOAM and Palabos were used for FVM and LB, respectively. Importantly, the parallel LKMC solver utilizes particle-based parallel decomposition allowing efficient use of cores over highly heterogeneous regions of the domain. The parallelized model was validated against a reference serial version for accuracy, demonstrating comparable results for both microfluidic and stenotic arterial clotting conditions. Moreover, the parallelized framework was shown to scale essentially linearly on up to 64 cores. Overall, the parallelized multiscale framework described here is demonstrated to be a promising approach for studying single-platelet resolved thrombosis at length scales that are sufficiently large to directly simulate coronary blood vessels.

A massively parallel implicit 3D unstructured grid solver for computing turbulent flows on latest distributed memory computational architectures

An implicit unstructured grid density-based solver–PRAVAHA based on a parallel variant of the lower upper symmetric Gauss-Seidel (LUSGS) method is developed to compute large-scale engineering problems. A four-layered parallel algorithm is designed to efficiently compute three-dimensional turbulent flows on massively parallel modern multiple instruction multiple data-stream (MIMD) computational hardware. This data parallel approach achieves multiple layers of parallelism including continuity of flow solution, transfer of solution gradients, and calculation of drag/lift/solution residuals, right up to the innermost implicit LUSGS solver sub-routine, which is relatively less explored in the literature. Domain decomposition is performed using the METIS software based on multi-level graph partitioning algorithms. Non-blocking message-passing interface library functions are used to manage inter-processor communication through explicit message passing, efficiently. Super-linear scalability of the parallel solver is established on the current state-of-the-art supercomputing facility, the 838 teraflops PARAM seva on up to 6144 cores. Linear or even super-linear speedup on problems of significant size is observed even on ad-hoc parallel computing platforms like workstations and multi-node clusters, for turbulent flow simulations.

Effective elastic properties of three-dimensional multiple crack problems with the isogeometric boundary element parallel fast direct solver

We propose an isogeometric boundary element (IGABEM) parallel fast direct solver based on OpenMP to solve three-dimensional multiple crack problems. In this paper, the orderly and randomly distributed cracks are studied to observe the influence of the multiple crack interaction on the effective elastic properties. This paper designs the parallel implementation of the matrix low rank approximation and the matrix assembly for the hierarchical off-diagonal low rank (HODLR) matrix. In the matrix low rank approximation, we propose the m-n tree to improve the accelerated hybrid algorithm to balance the CPU performance and memory usage. The numerical results show that the effective elastic properties can respond to the strong interaction to a certain extent, but the maximum stress intensity factors (SIFs) of multiple cracks still need to be calculated to diagnose the possible crack initiation points. On the other hand, the numerical results also show that the IGABEM parallel fast direct solver can greatly improve the computational efficiency on the premise of ensuring the computational accuracy.

Applying a Situational Analysis Solver to Problems Involving Umbra/Sunlit Model

The search for optimal time intervals for satellite operations performance is based on verifying specific conditions of geometric or physical nature. Several conditions are combined in a situational problem. To be able to solve different situational problems, it is necessary to develop program codes for verifying different situational conditions in advance. Two situational conditions for determining if the satellite is in the sunlit zone or the umbra based on the conical models of the Earth's shadow are presented. Problems with one or more conditions are solved by a developed parallel solver for situational analysis. Conditions checking the position of a satellite relative to the Earth's shadow can be combined with other situational conditions.

A Fully Implicit Parallel Solver for MHD Instabilities in a Tokamak

A Fully Implicit Parallel Solver for MHD Instabilities in a Tokamak

Fully-coupled parallel solver for the simulation of two-phase incompressible flows

In the framework of the in-house code Fugu, a fully-coupled solver is developed for massively parallel simulations of three-dimensional incompressible multiphase flows. The linearized momentum and continuity equations arising from the implicit solution of the fluid velocities and pressure are solved simultaneously. The method uses a BiCGStab(2) (Dongarra et al., 1998) iterative solver with an original preconditioner for the velocity block and an approximation of the inverse of the Schur complement. This is achieved by using PFMG or SMG from HYPRE and an efficient sparse matrix–vector multiplication using the CSR storage format. The construction and the tracking of the interface separating the different involved phases is based on a conservative VOF method. Test cases, such as a spherical bubble rising in quiescent liquid and the free fall of a dense sphere, are performed to validate the models, especially in the presence of strong density and viscosity ratios between fluids. Other cases, such as the phase inversion, demonstrate the ability of the new fully-coupled solver to solve two-phase problems with more than 1 billion degrees of freedom with excellent scalability.

The MPI + CUDA Gaia AVU–GSR Parallel Solver Toward Next-generation Exascale Infrastructures

We ported to the GPU with CUDA the Astrometric Verification Unit–Global Sphere Reconstruction (AVU–GSR) Parallel Solver developed for the ESA Gaia mission, by optimizing a previous OpenACC porting of this application. The code aims to find, with a [10, 100] μarcsec precision, the astrometric parameters of ∼108 stars, the attitude and instrumental settings of the Gaia satellite, and the global parameter γ of the parametrized Post-Newtonian formalism, by solving a system of linear equations, A × x = b , with the LSQR iterative algorithm. The coefficient matrix A of the final Gaia data set is large, with ∼1011 × 108 elements, and sparse, reaching a size of ∼10–100 TB, typical for the Big Data analysis, which requires an efficient parallelization to obtain scientific results in reasonable timescales. The speedup of the CUDA code over the original AVU–GSR solver, parallelized on the CPU with MPI + OpenMP, increases with the system size and the number of resources, reaching a maximum of ∼14×, >9× over the OpenACC application. This result is obtained by comparing the two codes on the CINECA cluster Marconi100, with 4 V100 GPUs per node. After verifying the agreement between the solutions of a set of systems with different sizes computed with the CUDA and the OpenMP codes and that the solutions showed the required precision, the CUDA code was put in production on Marconi100, essential for an optimal AVU–GSR pipeline and the successive Gaia Data Releases. This analysis represents a first step to understand the (pre-)Exascale behavior of a class of applications that follow the same structure of this code. In the next months, we plan to run this code on the pre-Exascale platform Leonardo of CINECA, with 4 next-generation A200 GPUs per node, toward a porting on this infrastructure, where we expect to obtain even higher performances.

Understand Restart of SAT Solver Using Search Similarity Index (Student Abstract)

SAT solvers are widely used to solve many industrial problems because of their high performance, which is achieved by various heuristic methods. Understanding why these methods are effective is essential to improving them. One approach to this is analyzing them using qualitative measurements. In our previous study, we proposed search similarity index (SSI), a metric to quantify the similarity between searches. SSI significantly improved the performance of the parallel SAT solver. Here, we apply SSI to analyze the effect of restart, a key SAT solver technique. Experiments using SSI reveal the correlation between the difficulty of instances and the search change effect by restart, and the reason behind the effectiveness of the state-of-the-art restart method is also explained.